SUMMARY Seismic hazard assessment (SHA) requires earthquake events characterized in terms of the moment magnitude (Mw) scale both in the earthquake catalogues and in the ground motion databases (SHA data sets). However, published Mw estimates for the same event may actually differ due to the adoption of different computation methods, input data, or seismic networks. The main objective of this paper is to develop a novel strategy to assign a unique Mw value for each earthquake and unified to an Mw reference data set that can be applied to low-to-moderate seismicity regions (Mw < 4.5) such as Metropolitan France, the target region of our study. The strategy consists of first collecting all Mw estimated directly by spectral or temporal inversion in a large area of the European–Mediterranean zone, including regional and specific studies in our target region. Then, the sources of Mw estimates are ranked in five different categories, from global to specific studies. A GCMT (Global Centroid Moment Tensor project) standard Mw value is recomputed and a quality flag is assigned depending on the level of the information provided by the sources. Mw estimates are then compared at the European–Mediterranean scale with those provided by the CMT services, chosen as reference. Mw estimates are subsequently corrected for their systematic deviations by progressively including lower magnitude estimates as one moves from high ranked categories to lower ones at each step of the unification procedure. In this work, the collected data set contains 6752 Mw estimates of 4454 shallow events (depth < 40 km) that occurred between 1963 and 2019 and computed by 34 sources (bulletins, publications,…, etc). A unified Mw value could be attributed to 185 events (2.36 ≤ Mw ≤ 5.35) in France and neighbouring regions and 3351 events (3.06 ≤ Mw ≤ 7.57) in the European–Mediterranean region. Finally, we showed that this Mw data set is consistent with European SHA data sets but leads to slightly larger Mw values compared to the French SHA data sets. We also noted that some variability still subsist in Mw data set compared to the existing SHA data sets, especially for Mw < 5.0. This new unified Mw data set is a first step toward the building of future catalogues. It will contribute to greatly improve the coherence of Mw definitions in the next generation of SHA data sets for both metropolitan France and Europe.